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Syllabus |
1. Topology and Geometry in R^n.
Inner product, norm, and distance. Cross product. Lines and planes. Quadratic forms. Basic topological notions.
2. Differential Calculus in R^n.
Scalar- and vector-valued functions.
Graphs and level sets. Continuity. Partial and directional derivatives. Tangent plane. Differentiability. Higher-order derivatives. Derivative of a composite function (chain rule). Taylor’s formula. Local and constrained extrema. Implicit Function Theorem.
3. Multiple Integrals.
Definition, Fubini’s theorem, and change of variables.
Double integrals: Cartesian and polar coordinates.
Triple integrals: Cartesian, cylindrical, and spherical coordinates. Applications.
4. Vector Calculus.
Line and surface integrals.
Green’s theorem, Stokes’ theorem, and Gauss’ theorem.
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Main Bibliography |
[1] Stewart, J., Cálculo, Volume 2, Tradução da 7.ª edição Norte-Americana, Cengage Learning Edições Ltda, 2014
[2] Marsden and Tromba, Vector Calculus, 6th Edition, W.H. Freeman, 2011
[3] Salas, Hille, Etgen, Calculus: One and Several Variables, 6th Edition, John Wiley & Sons, Inc, 2007
[4] Adams, R., Essex, C., Calculus, A Complete Course, 9th Edition, Pearson, 2018
[5] Kreyszig, Advanced Engineering Mathematics, 10th Edition, John Wiley & Sons, Inc, 2011
[6] Anton, H., Bivens, I., Cálculo, Volume 2, Stephen Davis, 8.ª Edição, Bookman, 2007
[7] Apostol, T., Cálculo, Volume 2, Reverté, 1994
[8] Pires, G., Cálculo Diferencial e Integral em R^n, IST Press, 2012
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